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Jan M. Pawlowski Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis 1
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Page 1: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Jan M. Pawlowski Universität Heidelberg & ExtreMe Matter Institute

Trento, November 14th 2012

Quantum fluctuations & magnetic catalysis

1

Page 2: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Heavy ion collisions

UrQMD Frankfurt/MStrickland

Simulation of a heavy ion collision

2

Page 3: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Functional Methods for QCD

Chiral symmetry breaking

Magnetic catalysis

Summary & Outlook

Outline

3

Page 4: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Functional Methods for QCD

FunMethods: FRG-DSE-2PI-...

Quarks Gluons

4

Page 5: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

RG-scale k: t = ln k

Functional Methods for QCD

free energy

JMP, AIP Conf.Proc. 1343 (2011)

gluequantum fluctuations

hadronic quantum fluctuations

quark quantum fluctuations

Yang-Mills:

Rk2R 2k2

k2p20

1

∂tΓk[A, c, c] =1

2Tr

1

Γ(2)[A, c, c] +Rk∂tRk

− ∂tCk

full propagator regulator

∂t = k ∂k

∂tΓk[φ] =

by L. Fister

dynamical

5

Page 6: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

RG-scale k: t = ln k

Functional Methods for QCD

Fermions are straightforward though ‘physically’ complicated

no sign problem

chiral fermions

Gluons have cost us decades

Complementary to lattice!

free energy

JMP, AIP Conf.Proc. 1343 (2011)

∂tΓk[φ] =

gluequantum fluctuations

hadronic quantum fluctuations

quark quantum fluctuations

bound states via dynamical hadronisation

dynamical

6

Page 7: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Naturally encorporates PQM/PNJL models as specific low order trunations

pure glue flow + + ...

flow of gluon propagator

Functional Methods for QCD

free energy

∂tΓk[φ] =

gluequantum fluctuations

hadronic quantum fluctuations

quark quantum fluctuations

JMP, AIP Conf.Proc. 1343 (2011)

7

Page 8: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Yang-Mills

!t = 2 + + +2

Functional Methods for QCD

Matter

- + 1

2

!t!1

= +

!t!1

= !!1/2

+

2PI-resummation

∂t = − 3 +6 +3 − 6

− 1

2+

Aconst0

Veff [σ,π;A0]

λψ

h[σ,π]

+matter-contributions

DSE

8

Page 9: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Chiral symmetry breaking

in strong magnetic fields

Quarks

9

Page 10: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

EOM(σ)

Chiral symmetry breaking

Perturbative four-fermi coupling

Nf = 2 : τ = (σ1,σ2,σ3)

λψ

2

(qq)2 + (iqγ5τq)

2

λψ ∝ α2s

σ = 0Bosonisation (Hubbard-Stratonovich)

q

q

λψ

2

(ψψ)2 + (iψγ5τψ)

2=

m2σ

2

x

σ2 + π2

+ i h

xψ(σ + iγ5τπ)ψ

∝ + + +λψ =

∝ ∝+ + +

bosonisation

10

Page 11: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

ΓΛ[ψ, ψ] = ψ ∂/ψ +1

2ψaαi ψbα

j ΓΛabcdijlm ψcβ

l ψdβm

τ : - generators SU(Nf ) ∝ +λψ = + +

Low energy effective action at high scales

Simplest approximation: NJL-model

+...

Chiral symmetry breakingLow energy effective models

ΓΛ[ψ, ψ] = ψ i∂/ψ − λΛ

2

(ψψ)2 + (iψγ5τψ)

2

11

Page 12: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Mean field free energy at one loop

βΩ/V −NcNfΛ4

4π2

1 +

1− 2π2

NcNf λΛΛ2

M2

Λ2

Chiral phase transition

Chiral symmetry breakingLow energy effective models

λΛΛ2 >

2π2

NcNf

M2 = −λΛψψ

12

Page 13: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Mean field free energy at finite temperature

βΩ/V −NcNfΛ4

4π2

1 +

1− 2π2

NcNf λΛΛ2

M2

Λ2

Chiral phase transition

Chiral symmetry breakingLow energy effective models

Tc =

3Λ2

π2− 6

NcNfλΛ

λΛΛ2 >

2π2

NcNf

1− π2

3

Λ2

T 2

critical temperature

M2 = −λΛψψ

T Λ

13

Page 14: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

M2 = −λΛψψ

Mean field free energy at finite temperature & magnetic field

Full sum

Chiral symmetry breakingLow energy effective models

βΩ/V = −Nc

f=u,d

|qfB|2π

dpz2π

ω0 + 2T ln

1 + e−βω0

+

M2

2λΛ

LLLA

2

p2≤Λ2

d3p

(2π)3f(ω) −→ 2

Λ,B

d3p

(2π)3f(ωn) ≡

|qB|2π

NΛ,B

n=0

αn

p2≤Λ2

pz2π

f

p2z + 2|qB|n+M2

14

Page 15: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

M2 = −λΛψψ

Mean field free energy at finite temperature & magnetic field

Chiral symmetry breakingLow energy effective models

critical temperature

βΩ/V = −Nc

f=u,d

|qfB|2π

dpz2π

ω0 + 2T ln

1 + e−βω0

+

M2

2λΛ

LLLA

Tc =2eγ

πΛ exp

− 2π2

Nc λΛ

f |qfB|

Chiral phase transition

λΛΛ2 > 0

T Λ

15

Page 16: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

λψ

Chiral symmetry breaking

Flow for four-fermion coupling with infrared scale λψ = λψk2 k

+ + + ...

∂tλψ

k∂kλψ 2λψ A

T

k

λ2ψ B

T

k

λψ αs C

T

k

α2s+ + + + ... =

Chiral symmetry breaking directly sensitive to size of αs

Chiral symmetry breaking in QCD within the FRG

16

Page 17: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

σ, π, ...q

qλψ

Chiral symmetry breaking

Flow for four-fermion coupling with infrared scale λψ = λψk2 k

k∂kλψ 2λψ A

T

k

λ2ψ B

T

k

λψ αs C

T

k

α2s+ + + + ... =

+ + + ...

∂tλψ

Dynamical hadronisation

Gies, Wetterich ’01 JMP ’05 Flörchinger, Wetterich ’09

dynamical

Dynamical hadronisation...and now for something completely different...

17

Page 18: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

∂th2

m2λψ

∂tλψ

Flow for four-fermion coupling with infrared scale λψ = λψk2 k

k∂kλψ 2λψ +

+ ...

= + +

++

+ - terms

Chiral symmetry breakingDynamical hadronisation

18

Page 19: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

∂th2

m2

= 0

k∂kλψ 2λψ +

+ ...

= + +

++

+ - terms

Full bosonisation λψ = 0

Chiral symmetry breaking

Meson potential

σπ

∂th2

m2

+ ...

+ - terms

Dynamical hadronisation

19

Page 20: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

h(k)

k[GeV]0.1 0.5 1.0 5.0 10.0 50.0 100.0

10

20

15 UV2 GeVUV5 GeVUV10 GeVUV90 GeV

initial scale

Full bosonisation λψ = 0

h(k)

k[GeV]

0.01 0.1 1 10 100

10

15

UV90 GeV, Ε100, ΛΣ0.001, h0.001UV90 GeV, Ε10, ΛΣ0.001, h0.001UV90 GeV, Ε4.89, ΛΣ0.001, h0.01UV90 GeV, Ε4.89, ΛΣ0.001, h0.1UV90 GeV, Ε4.89, ΛΣ0.001, h1UV90 GeV, Ε4.89, ΛΣ0.001, h0.001

initial conditions

Braun, Fister, Haas, JMP, in prep

Chiral symmetry breakingDynamical hadronisation

20

Page 21: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

h(k)

k[GeV]0.1 0.5 1.0 5.0 10.0 50.0 100.0

10

20

15 UV2 GeVUV5 GeVUV10 GeVUV90 GeV

initial scale

Full bosonisation λψ = 0

Low energy models

Braun, Fister, Haas, JMP, in prep

Chiral symmetry breakingStability of low energy models

21

Page 22: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

h(k)

k[GeV]0.1 0.5 1.0 5.0 10.0 50.0 100.0

10

20

15 UV2 GeVUV5 GeVUV10 GeVUV90 GeV

initial scale

Full bosonisation λψ = 0

Low energy models

FRG: (

com

plet

ely)

fixe

d from

QCD

Braun, Fister, Haas, JMP, in prep

Chiral symmetry breakingStability of low energy models

21

Page 23: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

λψ

Chiral symmetry breaking

Flow for four-fermion coupling with infrared scale λψ = λψk2 k

+ + + ...

∂tλψ

k∂kλψ 2λψ A

T

k

λ2ψ B

T

k

λψ αs C

T

k

α2s+ + + + ... =

Chiral symmetry breaking directly sensitive to size of αs

αs,eff → 0

Nc → ∞

h(k)

k[GeV]0.1 0.5 1.0 5.0 10.0 50.0 100.0

10

20

15 UV2 GeVUV5 GeVUV10 GeVUV90 GeV

initial scale

Λ

IR-stability

k < Λ

Chiral symmetry breaking in QCD within the FRG

22

Page 24: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

λψ

Chiral symmetry breaking

Flow for four-fermion coupling with infrared scale λψ = λψk2 k

+ + + ...

∂tλψ

k∂kλψ 2λψ A

T

k

λ2ψ B

T

k

λψ αs C

T

k

α2s+ + + + ... =

∂tλk = −NcNf λ2kk

2

3π2

∂tλk = 2λk − NcNf

3π2λ2k

Chiral symmetry breaking directly sensitive to size of αs

αs,eff → 0

Nc → ∞

Chiral symmetry breaking in QCD within the FRG

23

Page 25: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Fukushima, JMP ’12

∂tΠk(0) =

2Nc +

34

Nfk2

3π2

1

2− 1

eβk + 1− βk

eβk

(eβk + 1)2

t = + + · · ·+ +

(a) (b) (c) (d)

Πk(p) 2Nc 1 1/4-

Flow of four-point correlation function

Chiral symmetry breaking!t!k["] = 1

2! ! + 1

2

λΛΛ2

3>

2π2

NcNf

λk =λΛ

1 +NcNf λΛ

6π2(k2 − Λ2)

∂tλψ λk = Πk(0)

Chiral symmetry breaking in QCD within the FRG

24

Page 26: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Fukushima, JMP ’12

∂tΠk(0) =

2Nc +

34

Nfk2

3π2

1

2− 1

eβk + 1− βk

eβk

(eβk + 1)2

t = + + · · ·+ +

(a) (b) (c) (d)

Flow of four-point correlation function

Chiral symmetry breaking!t!k["] = 1

2! ! + 1

2

∂tλψ

Tc =

Λ2

π2− 6

NcNf λΛ

critical temperature

λk =λΛ

1 +NcNf λΛ

6π2

k2 − Λ2 + π2T 2

λk = Πk(0)

Chiral symmetry breaking in QCD within the FRG

25

Page 27: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Fukushima, JMP ’12

Flow of four-point correlation function

critical temperature

Integrated flow λk =λΛ

1 +Nc λΛ

2π2

f

|qfB| t

Chiral symmetry breakingStrong magnetic fields with RG in LLLA

!t!k["] = 1

2! ! + 1

2

Dimensional Reduction

λk = Πk(0)

Tc = 0.42Λ exp

− 2π2

NcλΛ

f |qfB|

t = + + · · ·+ +

(a) (b) (c) (d)

∂tλk = − Nc

2π2

f

|qfB|λ2k

26

Page 28: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Fukushima, JMP ’12

Flow of four-point correlation function

Chiral symmetry breaking!t!k["] = 1

2! ! + 1

2

µ = 0

0 0.1

0.2 0.3

0.4 0.5

0 0.2

0.4 0.6

0.8 1

1

10

100

Temperature T [ ]Magnetic Field |eB| [ 2]

*

0 0.1

0.2 0.3

0.4 0.5

0 0.2

0.4 0.6

0.8 1

1

10

100

Temperature T [ ]Magnetic Field |eB| [ 2]

*

λψ∗

µ = 0

0 0.1

0.2 0.3

0.4 0.5

0 0.2

0.4 0.6

0.8 1

1

10

100

Temperature T [ ]Magnetic Field |eB| [ 2]

*

λψ∗

NJL-model

t = + + · · ·+ +

(a) (b) (c) (d)

∂tλk = ∂tΠk(p = 0, B)

Strong magnetic fields with RG beyond LLLA

Skokov ’11PQM+

27

Page 29: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Fukushima, JMP ’12

Flow of four-point correlation function

Chiral symmetry breaking!t!k["] = 1

2! ! + 1

2Strong magnetic fields with RG with full non-localities

λk = Πk(0, B)

t = + + · · ·+ +

(a) (b) (c) (d)

!"##

!$##

!%##

#

# $ & ' ( %#!)*+

,-./01233456-7

/01233456-7)*+

λψ

bubble resummation

s, t & u channel

s-channel

LLL approximation

∂tλk = ∂tΠk(p = 0, B)

Πk(p) =λk(p)

1− λk(p)[Πk(p)−Πk(0)]

28

Page 30: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Summary & Outlook

29

Page 31: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

RG point of view of magnetic catalysis

magnetic catalysis via dimensional reduction

fluctuations & magnetic catalysis

momentum dependence

Gluonic fluctuations

B-dependence of strong coupling

dynamical hadronisation

Summary & outlook

Dimensional Reduction

µ = 0

0 0.1

0.2 0.3

0.4 0.5

0 0.2

0.4 0.6

0.8 1

1

10

100

Temperature T [ ]Magnetic Field |eB| [ 2]

*

0 0.1

0.2 0.3

0.4 0.5

0 0.2

0.4 0.6

0.8 1

1

10

100

Temperature T [ ]Magnetic Field |eB| [ 2]

*

λψ∗

!"##

!$##

!%##

#

# $ & ' ( %#!)*+

,-./01233456-7

/01233456-7)*+

λψ

30

Page 32: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Additional material

31

Page 33: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Confinement & Thermodynamics

Strickland

Fister, JMP

T =0T A

− p (T ; A) =

0

Λ

dk

k

32

Page 34: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

p2A A(p2)

perturbative

2

3

4

1

0 5 64321

!"!! #"$

%&!! #"$

!"!! '"(

'#!! '"(

%&!! '""

p [GeV]

FRG: Fischer, Maas, JMP ’08

lattice: Sternbeck et al. ’06

non-perturbative and phenomenologically

relevant

Propagators

Propagators phenomenologically well described in 1/N expansion

33

Page 35: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

p [GeV]

Longitudinal Propagator GL

FRG: T = 0

FRG: T = 0.361Tc

FRG: T = 0.903Tc

FRG: T = 1.81Tc

Lattice: T = 0

Lattice: T = 0.361Tc

Lattice: T = 0.903Tc

Lattice: T = 1.81Tc

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

p [GeV]

Transversal Propagator GT

FRG: T = 0

FRG: T = 0.361Tc

FRG: T = 0.903Tc

FRG: T = 1.81Tc

Lattice: T = 0

Lattice: T = 0.361Tc

Lattice: T = 0.903Tc

Lattice: T = 1.81Tc

Fister, JMP ’11

Lattice: Maas, JMP, Spielmann, von Smekal ’11

!t = 2 + + +2

!t!1

= +

!t!1

= !!1/2

+

+ RG-dressed gluonic vertices

ConfinementThermal gluon propagators

confirmed with the full system, JMP, Fister, in prep

see talk of L.Fister

34

Page 36: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4Tσ−1/2

0

0.1

0.2

0.3

0.4

0.5

0.6

DL(0

)−1/2

[GeV

]

322×4

642×4

1282×4

2562×4

1282×6

cT/T0 0.5 1 1.5 2

[GeV

]-1

/2(0

)LD

0

0.5

1

Electric screening mass for SU(2)

3d

4d

critical scaling in Landau gauge props on the lattice?

ν ≈ 0.68

ν ≈ 1

Maas, JMP, Spielmann, von Smekal ’11

ConfinementChromo-electric propagator

FRG

DL(0)−1/2 ∝ |T−Tc|ν + · · ·

DL(0)−1/2 ∝ V[A0] + · · ·

DL(0) = AAT(0)

global gauge fixing35

Page 37: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Confinement

Braun, Gies, JMP ‘07

SU(3)

βgA0

-0.5-0.4-0.3-0.2-0.1

0 0.1 0.2 0.3 0.4

0 0.2 0.4 0.6 0.8 1

!4 V(!

<"

0>)

! <A0>/(2#)

0.3 0.5 0.7

276 MeV

295 MeV

286 MeV

280 MeV

276 MeV

271 MeV

β4 VYM[A0]

Tc = 276± 10MeV

Order parameter

Φ[43π

1βg

] = 0

Φ

0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25

0.0

0.2

0.4

0.6

0.8

1.0

SU(3)

T/Tc

Polyakov loop

lattice : Tc/√

σ = 0.646

Φ[A0] =13(1 + 2 cos

12βgA0)

Tc/√

σ = 0.658± 0.023

SU(N), Sp(2), E(7): Braun, Eichhorn, Gies, JMP ’10

SU(2) & critical scaling: Marhauser, JMP ’08

36

Page 38: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

pGT=0,k ∂tRk

T =0T A

− p (T ; A) =

0

Λ

dk

k

Confinement & Thermodynamics

FRGBorsanyi et al.

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.2

0.4

0.6

0.8

1.0

TTc

p YMp SB

A0,min

p

GT ,k ∂tRk

pre

lim

inary

Fister, JMP, in prep

1/2 * 2 polarisations

37

Page 39: uni-regensburg.de - Jan M. Pawlowski Universität …eng14891/qcdB...Universität Heidelberg & ExtreMe Matter Institute Trento, November 14th 2012 Quantum fluctuations & magnetic catalysis

Full dynamical QCDPhase structure

0

0.2

0.4

0.6

0.8

1

150 160 170 180 190 200 210 220 230

T [MeV]

f!(T)/f!(0)

Dual density

Polyakov Loop

160 180 200

"L,d

ual

0

0.2

0.4

0.6

0.8

1

1 1.5 2 2.5 3

T/Tc

Lren(T)

HISQ: N =8N =6

stout cont.SU(3)

Polyakov loopChiral condensate

Budapest-Wuppertal ’10 hotQCD ’10

Braun, Haas, Marhauser, JMP ‘09

0

50

100

150

200

0 50 100 150 200 250 300 350

T [M

eV]

µ [MeV]

χ crossoverΦ crossover—Φ crossoverCEPχ first order

Phase diagram of quantised PQM-model

Herbst, JMP, Schaefer ’10

Nf =2 & chiral limit

FRG QCD results at finite density

Braun, Fister, Haas, JMP, in prep

FRG QCD surveyJMP, Aussois ’12

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